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Programming Articles
Page 546 of 2547
Find four missing numbers in an array containing elements from 1 to N in Python
Finding missing numbers in an array is a common programming problem. When we have an array of distinct numbers from range [1, N] with size (N-4), exactly four numbers are missing. This problem can be solved efficiently using array manipulation techniques. Problem Understanding Given an array of distinct numbers where: Each number lies in range [1, N] Array size is (N-4) No element is repeated We need to find 4 missing numbers in sorted order For example, if A = [2, 8, 4, 13, 6, 11, 9, 5, 10], then N = 13 and the ...
Read MoreFind First element in AP which is multiple of given Prime in Python
In this problem, we need to find the position of the first element in an Arithmetic Progression (AP) that is divisible by a given prime number. Given the first term A, common difference D, and prime number P, we use modular arithmetic to efficiently find this position. For example, if A = 3, D = 4, P = 5, the AP terms are: 3, 7, 11, 15, 19... The fourth term (15) is the first multiple of 5, so the answer is 3 (0-indexed position). Algorithm Approach The solution uses Fermat's Little Theorem and modular exponentiation. For ...
Read MoreFind element position in given monotonic sequence in Python
When working with monotonic sequences, we often need to find the position where a specific value occurs. This problem involves a monotonic increasing sequence defined by the function f(m) = am + bm[log₂(m)] + cm³, where [log₂(m)] represents the floor of log base 2. Understanding the Formula The sequence function f(m) = am + bm[log₂(m)] + cm³ contains three components: Linear term: am (where a = 1, 2, 3, ...) Logarithmic term: bm[log₂(m)] (where b = 1, 2, 3, ...) Cubic term: cm³ (where c = 0, 1, 2, 3, ...) The floor logarithm ...
Read MoreFind Duplicates of array using bit array in Python
Suppose we have an array of n different numbers; n can be 32, 000 at max. The array may have duplicate entries and we do not know what is the value of n. Now if we have only 4-Kilobytes of memory, how would display all duplicates in the array? So, if the input is like [2, 6, 2, 11, 13, 11], then the output will be [2, 11] as 2 and 11 appear more than once in given array. How Bit Array Works A bit array uses individual bits to track whether a number has been seen ...
Read MoreFind distinct elements common to all rows of a matrix in Python
Finding distinct elements common to all rows of a matrix is a useful operation in data analysis. We need to identify elements that appear in every row of the matrix, regardless of their position. So, if the input matrix is: 13 2 15 4 17 15 3 2 4 36 15 2 15 4 12 15 26 4 3 2 2 19 4 22 15 Then the output will be [2, 4, 15], as these elements appear in all rows. Using Set ...
Read MoreFind d to maximize the number of zeros in array c[] created as c[i] = d*a[i] + b[i] in Python
Given two arrays A and B of n integers, we need to create array C where C[i] = d*A[i] + B[i] and d is any real number. Our goal is to find the value of d that maximizes the number of zeros in array C. For C[i] to be zero, we need d*A[i] + B[i] = 0, which gives us d = -B[i]/A[i] (when A[i] ≠ 0). Algorithm The approach is to ? Calculate possible values of d for each element where A[i] ≠ 0 Count frequency of each d value using a dictionary Handle ...
Read MoreFind combined mean and variance of two series in Python
When working with two separate data series, you often need to find the combined mean and combined variance of the merged dataset. This is useful in statistics when combining samples from different populations or datasets. The combined mean is calculated as a weighted average of individual means, while the combined variance uses the formula that accounts for both individual variances and the differences between individual means and the combined mean. Mathematical Formula For two series A1 and A2 with sizes n and m respectively: Combined Mean: (n × mean₁ + m × mean₂) / (n ...
Read MoreFind the minimum sum of distance to A and B from any integer point in a ring of size N in Python
We need to find the minimum sum of distances from any integer point X to two given points A and B on a ring of size N. The goal is to position X such that the total distance (distance from X to A + distance from X to B) is minimized, where X cannot be the same as A or B. In a ring structure, we can move in two directions: clockwise and counter-clockwise. The optimal position for X will depend on which path gives us the minimum total distance. Example Walkthrough If N = 30, A ...
Read MoreFind the minimum positive integer such that it is divisible by A and sum of its digits is equal to B in Python
Given two numbers A and B, we need to find the minimum positive integer M such that M is divisible by A and the sum of its digits equals B. If no such number exists, return -1. For example, if A = 50 and B = 2, the output will be 200 because 200 is divisible by 50 and the sum of its digits (2 + 0 + 0 = 2) equals B. Approach We'll use a breadth-first search (BFS) approach with the following strategy ? Use a queue to explore numbers digit by digit ...
Read MoreFind the minimum of maximum length of a jump required to reach the last island in exactly k jumps in Python
Suppose we have an array A of numbers, where the i-th number represents the position of an island. Given another integer k (1 ≤ k < N), a person standing on the 0-th island must reach the last island in exactly k jumps. We need to find the minimum of the maximum jump length required for this journey. All island positions are given in ascending order. For example, if A = [7, 20, 41, 48] and k = 2, the output will be 28. There are two possible paths: Path 1: 7 → 20 → 48 (jumps: ...
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